11 problems

Let $G$ be a graph with vertex set $V(G)$, and let $\sigma$ be a position of the parallel chip-firing game on $G$. If $p(\sigma)$ denotes the period of $\sigma$, then Bitar's conje…

For a graph with fixed boundary values, consider the $\ell^p$-energy minimizing dynamics and let the $\epsilon$-approximation time denote the time required to reach $\epsilon$-appr…

Majority Dynamics conjecture. For every $varepsilon>0$, with high probability the number of oscillating vertices lies in

Generic discreteness conjecture. For a generic graph $G$ and a generic function $f\in\mathcal A$, the set $X_{G,f}$ is discrete.

Let $G$ be a locally cyclic graph with boundary and minimum degree $\delta\ge 4$ triangulating a disc. Such a graph is clique null if its clique dynamics converges to the one-verte…

Let $G$ be a locally cyclic graph of minimum degree $\delta\ge 4$ triangulating a closed surface of Euler characteristic $\chi\ge 0$; equivalently, the surface is a sphere, project…

Majority dynamics assigns each vertex a state in a finite state set and updates states synchronously according to the majority of its neighbors. A trajectory stabilises to periodic…

Antimorphic-digraph tau-sequence conjecture. The $R$-systems associated with antimorphic digraphs possess strong $\tau$-sequences $Y(t)$ with the substitution

Let $\Gamma_n$ be the graph considered in the paper, and let $\mathcal{S}_n^\star$ be the distinguished update system supported on $\Gamma_n$, with preferred state $\star$. A point…

Let $\Gamma$ be a finite directed acyclic graph. Its universal dynamics monoid $D(\Gamma)$ is the smallest quotient of $\operatorname{\mathbf{HK}}_\Gamma$ through which all evaluat…

Let the dynamics evolve on a finite torus under fully asynchronous updates, and let the average convergence time be the average time to reach a limit set. Polynomial convergence-ti…